zoukankan      html  css  js  c++  java
  • 三分 Error Curves

    - Error Curves
    Time Limit:2000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u
    Submit Status

    Description

    Josephina is a clever girl and addicted to Machine Learning recently. She 
    pays much attention to a method called Linear Discriminant Analysis, which 
    has many interesting properties. 
    In order to test the algorithm's efficiency, she collects many datasets. 
    What's more, each data is divided into two parts: training data and test 
    data. She gets the parameters of the model on training data and test the 
    model on test data. To her surprise, she finds each dataset's test error curve is just a parabolic curve. A parabolic curve corresponds to a quadratic function. In mathematics, a quadratic function is a polynomial function of the form f(x) = ax2 + bx + c. The quadratic will degrade to linear function if a = 0. 



    It's very easy to calculate the minimal error if there is only one test error curve. However, there are several datasets, which means Josephina will obtain many parabolic curves. Josephina wants to get the tuned parameters that make the best performance on all datasets. So she should take all error curves into account, i.e., she has to deal with many quadric functions and make a new error definition to represent the total error. Now, she focuses on the following new function's minimum which related to multiple quadric functions. The new function F(x) is defined as follows: F(x) = max(Si(x)), i = 1...n. The domain of x is [0, 1000]. Si(x) is a quadric function. Josephina wonders the minimum of F(x). Unfortunately, it's too hard for her to solve this problem. As a super programmer, can you help her?
     

    Input

    The input contains multiple test cases. The first line is the number of cases T (T < 100). Each case begins with a number n (n ≤ 10000). Following n lines, each line contains three integers a (0 ≤ a ≤ 100), b (|b| ≤ 5000), c (|c| ≤ 5000), which mean the corresponding coefficients of a quadratic function.
     

    Output

    For each test case, output the answer in a line. Round to 4 digits after the decimal point.
     

    Sample Input

    2 1 2 0 0 2 2 0 0 2 -4 2
     
     1 #include <stdio.h>
     2 #include <string.h>
     3 #include <algorithm>
     4 using namespace std;
     5 
     6 const double inf=0x3f3f3f3f;
     7 const double eps=1e-9;
     8 
     9 int n;
    10 double a[10005],b[10005],c[10005];
    11 
    12 double C(double x)
    13 {
    14     double ma=-inf;
    15     for(int i=1;i<=n;i++)
    16     {
    17         double y=x*x*a[i]+x*b[i]+c[i];
    18         if(y>ma)
    19             ma=y;
    20     }
    21     return ma;
    22 }
    23 
    24 int main()
    25 {
    26     int T;
    27     int i,j,k,l;
    28     scanf("%d",&T);
    29     while(T--)
    30     {
    31         scanf("%d",&n);
    32         for(i=1;i<=n;i++)
    33         {
    34             scanf("%lf %lf %lf",&a[i],&b[i],&c[i]);
    35         }
    36         double lb,ub,mid,mmid,mid_value,mmid_value;
    37         lb=0,ub=1000;
    38         while(lb+eps<ub)
    39         {
    40             mid=(lb+ub)/2;
    41             mmid=(mid+ub)/2;
    42             mid_value=C(mid);
    43             mmid_value=C(mmid);
    44             if(mid_value<=mmid_value)
    45                 ub=mmid;
    46             else
    47                 lb=mid;
    48         }
    49         printf("%.4lf
    ",C(ub));
    50     }
    51     return 0;
    52 }
    View Code
  • 相关阅读:
    pyqt 实现左列表向右列表添加
    python 获取ffmpeg里可以推送的音视频设备名称
    精确控制windows全局音量二(Python)
    精确控制windows全局音量(Python)
    ${pagecontext.request.contextpath}绝对路径理解
    eclipse中修改JSP模板中的默认编码
    hibernate的ddl-auto属性
    乱码-eclipse显示中文16进制的
    在写数据库相关项目时,出现The server time zone value '�й���׼ʱ��' is unrecogni异常。
    mysql5.7.28安装和配置
  • 原文地址:https://www.cnblogs.com/cyd308/p/4681860.html
Copyright © 2011-2022 走看看